1. Field of the Invention
This invention relates to computed tomography, and more particularly to fan beam reconstruction techniques.
2. Discussion of the Prior Art
Computed tomography includes the fields of transmission computed tomography and emission computed tomography. In one form of fan beam transmission computed tomography, an X-ray source and a multi-channel detector are fixed with respect to each other and mounted for rotation on a gantry on opposite sides of a patient aperture. During the course of a scan, a number of projections are taken which are later convolved and back projected to produce a pixelized image representing the linear attenuation coefficients of the slice of the body through which the radiation had passed. The geometry of the system is such that the center of rotation of the source-detector assembly is intended to lie on the midline of the fan beam, on a line from the focal point of the source to a predetermined point on the detector.
In emission computed tomography, gamma emitting substances are ingested or injected into the body, following which the body is scanned to detect the concentration and distribution of the radioactive sources by taking projections at a plurality of angles around the body. An example of fan beam emission computed tomography is the rotating gamma camera used with a converging collimator. The collimator is intended to converge at a focal point, and the center of rotation of the collimater and gamma camera is intended to lie on the midline of the fan beam, on a line joining the focal point to a predetermined point on the detector.
The fan beam reconstrution algorithms in use are based on the assumption that the center of rotation of the system is as described above, that is, colinear with a line joining the focal point onto a known point on the detector. When the actual center of rotation is shifted from the midline of the fan, the effect will be artifacts in the reconstruction because the assumptions underlying the algorithm have not been met. In the parallel beam case, it is possible to simply shift the projections prior to processing in order to account for the new center of rotation. However, the fan beam case cannot be corrected by a simple shift, unless of course one rebins the fan beam projections into parallel beam projection sets. Rebinning, however, is considered to be computationally expensive and degrades resolution.
One of the factors which must be accounted for in true fan beam reconstruction algorithms is the diverging nature of the fan beam itself. The normal form of the Radon inversion relationship, on which many reconstruction techniques depend, assumes parallel beam geometry. When fan beam projections are reconstructed, geometric factors are required which account for the relationship between the parallel rays and the diverging rays. That relationship is typically accounted for in or just prior to the convolution operation as well as in the back projection operation which must map the data according to the geometry of the system. However when the center of rotation of the system is shifted, the system geometry is altered, and the standard pre-convolution and back projection factors are no longer directly applicable.
Typically in a transmission CT system as manufactured, the center of rotation will be in its expected location because the gantries of transmission CT systems, which include the X-ray source and detector array, can be constructed with great precision. If the geometry shifts over time, due to mechanical wear or the like, it is a relatively simple task to make measurements during the course of a scan to determine the magnitude of the shift. By way of analogy, in emission CT the detector, including its converging collimator array, cannot be manufactured with comparable precision and thus a shift in geometry including the location of the center of rotation is to be expected. In parallel hole (i.e., parallel beam) systems it is relatively easy to take calibrating measurements to determine the magnitude of the shift. However, up to now there has not been an easy way to accurately measure the magnitude of the shift in a converging collimator (i.e., fan beam) emission CT system.